两个平面交于一点

hbghlyj

math.stackexchange.com/questions/4878286/ 提到了一个问题：

For instance, one I was working on recently was:

"In a projective space of dimension four, $\mathbb{P}_4$, let $\pi_1, \pi_2$ be two planes that intersect at point, $\pi_1 \cap \pi_2 = \{p\}$, and let $r$ be a line that passes through $p$ and that isn't contained in $\pi_1$ nor in $\pi_2$. Prove that there exists a unique plane $\pi$ that contains $r$ and s.t. the intersections $\pi \cap \pi_1$, $\pi \cap \pi_1$ are lines."

如何证明呢？

hbghlyj

2019年有人提问：math.stackexchange.com/questions/3272474

Consider $3$ planes $\pi_1, \pi_2, \pi_3$ in the projective space $\mathbb{R}P^4$. They intersect two by two in a point. All the $3$ planes together spans the projective space and $\pi_1 \cap \pi_2 \cap \pi_3 = \emptyset$. Now I want to show there exists a unique plane $\pi_0$ which intersect the other planes in a line such that $\pi_0 \cap \pi_i$ is a line for $i = 1,2,3$.

是否和上面的题有关呢？